How to smooth/bend a specific edge?
Bevel

Easiest way for your particular case is probably to use the Bevel operator (other softwares sometime call this operation Charmfer) you can find in the Edge section of the Mesh sub-menu.

Other possible ways could be to use SubSurf modifier with proper crease or take advantage of capped&amp;extruded curves, but for the example you bring in, these kind of approaches don't look particularly helpful.



You can find an in-depth explanation of the usage the the Blender reference manual's page, but basically you should:


enter edit mode
select the eges you would like to bevel
run the command from the menu or press Crtl+B
adjust the size with the mouse cursor
increase the number of segments with the mousewheel
click to confirm


You can change the parameters even in the panel of the toolshelf on the lower left (or in the pop up menu you can call with F6).